I swear this is the truth. Tonight, I was about to pull the hard drive, disc drives and the network card for later use, leaving the chassis for recycling. (Don't throw these away; computers are full of toxic metals.) The RAM was already out -- I thought I had fried it with static or something -- but my intuition told me to put it back in and give it one more try. I also pressed in place every connector I could get my hands on. But I wasn't hopeful and didn't even plug the monitor in.
As it was booting up -- it would power up each time -- it beeped. One little beep, suggesting the BIOS, which hadn't been loading, loaded. I scrambled to get the monitor plugged in, to find the Kubuntu login screen. Shut it down, add ethernet and the new keyboard and mouse, and rebooted.
Voila! My computer is back. Hurrah! But boy the Mac Mini was little, cute and quiet.